Interview Evaluating inferences questions and answer of Reasoning

Interview Evaluating inferences questions and answer of Reasoning

Evaluating inferences (updated)

One of the most challenging areas in logical reasoning is evaluating inferences.  Here a passage will be followed by a few statements.  A student has to identify, whether the given statements are Definitely true, Probably true,   uncertain, probably false or Definitely false in the light of the passage.

Before going through the examples,let us try to recap some fundamentals of logic.  An inference is a conclusion based on the known facts.   An inference is definitely true when all the facts clearly supports the conclusion.  But an inference is probably true, when an inference is almost true with a few exceptions.

Example: 
In the last thirty years, the annual milk production has more than trebled to 69 million tonnes in 1996.  This extraordinary transformation of dairying in what has been described as a rags - to - riches story has led to milk being compared to the 'cinderella' of Indian agriculture.  While what has been achieved is impressive, the prospects ahead are challenging.  In the Indian context, one dimension of dairy development that has been equally significant as has been the phenomenal growth in milk production is its impact in upgrading the life of the rural poor.  
1. There has been a three hundred percent increase in milk production in India
2. India has always been a high quantity - milk producing nation
3. India produces more cow's milk than buffalo milk
4. The rural poor are happier than before
5. India has been producing milk for the last thirty years.  

Analysis:
1. There has been a three hundred percent increase in milk production in India
In the last thirty years, the annual milk production has more than trebled to 69 million tonnes in 1996.  This extraordinary transformation...........
From the above lines it is clear that the production has been trebled. That is the initial production could be 69/3 = 23 million tonnes.  So percentage increase in the production is (69 - 23)/23 X 100 = 200%.
So the above inference is clearly false.

2. India has always been a high quantity - milk producing nation
In the last thirty years, the annual milk production has more than trebled to 69 million tonnes in 1996.This extraordinary transformation of dairying in what has been described as a rags - to - riches story has.......
This extraordinary transformation suggests that India's milk production has increased in great quantity and the rags - to - riches line suggests that India is not producing milk in great quantities in the earlier days and our discussion is limited to the 30 year period in the above passage, and we don't have enough information about the earlier periods.   So the qualifier "always" in the question makes this a false statement.  But may be 23 million tonnes is a great quantity too.  So we should say this statement is "probably false".

3. India produces more cow's milk than buffalo milk
Simple one.  No information was provided in the passage about types of milk.  Uncertain

4. The rural poor are happier than before
This extraordinary transformation of dairying in what has been described as a rags - to - riches story ............... While what has been achieved is impressive, the prospects ahead are challenging.............. its impact in upgrading the life of the rural poor.  
The rags to riches suggests that it created good income and we could say that there is a change in the life style of people.  But the last line suggests the underlying challenge.  So in the light of above two statements we could safely conclude that the statement is probably true.

5. India has been producing milk for the last thirty years.
In the last thirty years, the annual milk production has more than trebled to 69 million tonnes in 1996.
Definitely true.

Example: 
Independent testing of certified products is an essential feature of the BIS certification Marks scheme.  For this purpose, BIS has a network of eight laboratories in the country, Which are in a position to issue around 42000 test reports in a year.  These laboratories are being constantly expanded and their testing facilities augmented and modernized.  BIS has also recognized around 280 laboratories belonging to public and private sectors for testing products under its certification scheme. 
1. The BIS Scheme does not test uncertified products. 
2. Every laboratory of the BIS can issue more than 4000 test reports in a year
3. The BIS has no dynamism in its workings
4. The BIS is an autonomous body
5. Certification is a process that needs to be constantly modernized. 
Analysis:
1. The BIS Scheme does not test uncertified products.
Independent testing of certified products is an essential feature of the BIS certification Marks scheme.
The wording in the red letters suggests that BIS testing of certified products is its essential feature.  But it does not mean that it may not test uncertified products.  So the statement is uncertain

2. Every laboratory of the BIS can issue more than 4000 test reports in a year
BIS has a network of eight laboratories in the country, Which are in a position to issue around 42000 test reports in a year. 
42000 reports by 8 laboratories is 5250 reports on an average. But we could not say each laboratory may produce more than 5250 reports or not.  Some may be small and produce less than 5250, and some laboratories may be big to produce 10,000.  Now the problem is shall we classify this statement as uncertain, or probably false, or probably true (Surely not definitely true or false).

Now look at the question statement.
Every laboratory of the BIS can issue more than 4000 test reports in a year
Here author is saying every laboratory "can issue".  That means he is talking about possibility. Had he used only "issue" then the statement is uncertain as we need more information like whether all laboratories are in same magnitude or not.  So here he is talking about possibility and there are more chances that this probability is true.  But we are not certain that this is 100% true.  So this statement is probably true.

3. The BIS has no dynamism in its workings
 These laboratories are being constantly expanded and their testing facilities augmented and modernized. 
This line suggests that the above statement is definitely false as the expansion and modernization suggests dynamism.

4. The BIS is an autonomous body
Independent testing of certified products is an essential feature of the BIS certification Marks scheme. 
The independent testing suggests that it has autonomy to test products but we cannot safely conclude that it is an autonomous body or not. Probably true.

5. Certification is a process that needs to be constantly modernized.
These laboratories are being constantly expanded and their testing facilities augmented and modernized
If there is no necessity why BIS had constantly expanded and modernized its facilities? Defineitely True

Example: 

The economic reforms programme is going to affect not only the private industrial sector but also the public sector.  Many people associate the economic restructuring programme with privatisation.  This is one area of economic reforms where India has chosen to tread cautiosly.  The process of privatisation has been set in motion by the disinvestment campaign in the public sector.  Public sector industries in India have been incurring losses over long periods while their counterparts in the private sector are making profits.  The economic reforms programme in India will be incomplete without a restructuring of the punblic sector undertakings. 
1. The greater emphasis of reforms is on the private sector probably true
2. India's approach towards reforms is cautious true
3. The reforms have not intended to restructure the public sector units false
4. Economic restructuring programme means privatisation false
5. Disinvestment of public sector is a part of econimic restructuring true
Analysis:
1. The greater emphasis of reforms is on the private sector
The economic reforms programme is going to affect not only the private industrial sector but also the public sector.  It is clear from the above that economic reforms mainly intended for private sector, besides having some impact on the public sector.  Not only --- but also is a co-ordinating conjunction which gives equal emphasis to both the clauses. So we cannot say that the emphasis is on private sector.  It creates some ambiguity. So the above said statement is probably true

2. India's approach towards reforms is cautious true
This is one area of economic reforms where India has chosen to tread cautiously.  Definitely true

3. The reforms have not intended to restructure the public sector units
The economic reforms programme is going to affect not only the private industrial sector but also the public sector. .............The economic reforms programme in India will be incomplete without a restructuring of the public sector undertakings.   Author clearly mentioned in the first line that the reforms are having some impact on the public sector too.  and also in the last line he asserted that reforms program is incomplete without restructuring of public sector units.  So the above said statement is definitely false

4. Economic restructuring programme means privatization false
Many people associate the economic restructuring programme with privatisation.  This is one area of economic reforms where India has chosen to tread cautiosly. 
Even though many people think that economic restructuring and privatization are synonymous, but the author is correcting them in the succeeding line saying that this is only one area of economic reforms.  Definitely false

5. Disinvestment of public sector is a part of economic restructuring
The process of privatization has been set in motion by the disinvestment campaign in the public sector.  Definitely true

Interview Logical Consistency questions in Reasoning

Interview Logical Consistency questions in Reasoning

Suppose your father promised you a new bike, if you get good marks in your engineering.  What if, you don't get good marks? Our analysis explore possibilities of your father buying a new bike for you, even if you don't get good marks!  This type of reasoning is classified under a head called "Logical Consistency"

If ..., Then ....:

Let us take an example: If it rains, It will be cloudy

Let us explore the above statement in various cases
Case 1: It rained then we say, It should be cloudy.  So If x happened then y should happen. x ⇒ y
Case 2: There are no clouds, So there is no rain. ∼ y ⇒ ∼ x
Case 3: It is not raining.  Uncertain.  As there may be clouds or may not be.
Case 4: It is cloudy. Uncertain. As it may rain may not rain.

So of the above 4 cases Case 1 and Case 2 holds good.

Other Structures:

Only If:

Let us take an example, Only If you work hard, you will be successful.

Write the above statement like below. whenever there is 'onlyif' make sure it is in the middle of the two given statements.

Now to become successful, there is only one condition. To work hard. So we say, If one is succeeded means he must have work hard. So x ⇒ y
Also you did not work hard means, you are not succeeded. ∼ y ⇒ ∼ x

When / Whenever:
When / Whenever is same as If.  When x then y.
So possible conclusions are
1. x ⇒ y
2. ∼ y ⇒ ∼ x

Unless : 
Unless means "If not"
Unless you work hard, you fail = If you don't work hard, then you fail.
Again x ⇒ y and ∼ y ⇒ ∼ x are true

Either / or : 

Take the Proposition: Either I will drink Pepsi or I will eat a sandwich.  Let 'I will drink Pepsi' be 'X' and 'I will eat a sandwich' be 'Y'.
I drank Pepsi, then one cannot say whether I ate sandwich or not. But If did not drink Pepsi, then one can say that I must have eaten sandwich. So

Possible conclusions:
1. ∼ x ⇒ y
2. ∼ y ⇒ x

Solved Examples

1. Sam is either black or white.

A. Sam is not white  B. Sam is white

C. Sam is black. D. Sam is not black.

a. CB b. BA

c. DB d. DC

Solution:  We know that If not black then White or If not white then black. So AC or DB correct.  Correct option C.

 2. Rohit is in the class when Puneet is in the lab.

A. Puneet is in the lab.

B. Rohit is in the park.

C. Puneet is not in the lab.

D. Rohit is in the class.

a. CA b. AD

c. BC d. BD

Solution: When X then Y.  So When puneet is in the lab, then Rohit is in the class or Rohit is not in the class then Puneet is not in the lab. So AD is correct.

 3. You will add more value to the brand if strategic planning is done.

A. Stratigic planning was done.

B. More value was not added to the brand.

C. More value was added to the brand.

D. Stratigic planning was not done.

a. BD b. DB

c. BC d. DC

Solution: If strategic planning was done then you added more value to the brand or you did not add more value then Strategic planning was not done. So AC or BD correct. So choice A.

 4. She sleeps only when her boss is away from the office.

A. The boss is away B. She did not sleep.

C. She slept. D. The boss ins in the office.

a. DB b. AB

c. DC d. BC

Solution: Only when X then Y means Y happen then X happens or its contra positive X did not happen then Y did not happen. So We say She slept means boss is away, or Boss is not away then She did not sleep.
Option A.

 5. If Berty and Oly are selected in that order, Phil and Santhi cannot be selected.

A. Phil and Santhi are selected in that order.

B. Oly and Berty are selected in that order.

C. Berty and Oly are selected in that order.

D. Phil and Santhi are not selected.

a. BC b. CD

c. BD d. DB

Solution: this is called compound hypothetical.  If A and B then not C and D, Then C and D then not A or not B. Option B

Level 2

6.  My house has got a number.  
If it is a multiple of 3, then it is in between 50 and 59.
If it is not a multiple of 4, then it is in between 60 and 69
If it is not a multiple of 6, then it is in between 70 to 79
What is my house number?
Solution:  If the house number has to be in 50 to 59, then "If "conditions 2nd and 3rd statements should not happen. i.e., It is a multiple of 4 and 6.  Now we know that if a number is a multiple of both 4 and 6, then it is a multiple of 12.  But no 12 multiple exists between 50 to 59.  So house number should not be in between 50 to 59
If the house number has to be in 60 to 69, then "if" conditions of 1st and 3rd statements should not happen.  i.e., the number should not be a multiple of 3 but multiple of 6. All multiple of 6 should be multiples of 3.  So no number exists in between 60 to 69
So the house number should exists between 70 to 79.  Then It should not be a multiple of 3 but multiple of 4.   Between 70 to 79, 72 and 76 are multiples of 4 but only 76 is not a multiple of 3.  So my house number is 76

Interview Blood Relations questions and answer

Interview Blood Relations questions and answer  

To solve the blood relation questions easily we need to observe the family tree. 

If you assume you are in the middle then in your generation, you have sisters, brothers, cousins, Brother-in-law, sister-in-law. you can easily observe in each generation which of the relations you might have.

In solving the blood relation problems we usually assume the speaker is in the position "you" and try to prepare the diagram according to the question.

It is always best practice to denote Males and Females with notation.

Some general Relationships:

1. Brother                  Son of Mother or Father
2. Sister                     Daughter of Mother or Father
3. Aunt                      Sister of Mother or Father
4. Uncle                     Brother of Mother or Father
5. Cousin                   Son of Uncle or Aunt or Daughter of Uncle or Aunt
6. Grandmother         Mother of Father or Mother
7. Grandfather           Father of Father or Mother
8. Niece                     Daughter of Brother or Sister
9. Nephew                 Son of Brother or Sister
10.  Brother-in-law    Sister’s Husband or Brother of Wife or Husband
11. Sister-in-law        Brother’s Wife or Sister of Wife or Husband
12. Daughter-in-law  Wife of Son

Practice Problems

Solved Example 1:

Pointing to a man, a lady says that his father is the third son of her grandmother. How is the lady related to that man?

Ans: Pointing to a man, a lady says that his father is the third son of her grandmother.

Always the question consists of two parts. The phrase before "is"  and the phrase after "is".  Firstlydraw the seperate diagrams for these two phrases and merge them.

Pointing to a man  a lady says that his father: 

the third son of her grandmother: 

 Son of her grand mother means, that person is the lady's father or uncle.  

Merge the two diagrams above.  To the man the lady is pointing is son of one of these 3 sons. 

If the lady and the man has children of two different people then they are cousins, otherwise they are siblings.  So the lady is either cousin or sister to the man. 

Solved Example 2:

Introducing a woman, a man said, “Her mother’s husband’s sister is my aunt.” How is the man related to that woman?

Sol: Introducing a woman, a man said, “Her mother’s husband’s sister is my aunt.

“Her mother’s husband’s sister: 

 My aunt: Aunt is father's sister or Mother's sister

 By merging these two diagram's we get two cases

So the man is either brother or cousin to that woman. 

Solved Example 3:
Pointing to a photograph a lady tells Chetan, “I am the only daughter of this lady and her son is your maternal uncle.” How is the speaker related to Chetan’s father?

Pointing to a photograph a lady tells Chetan, “I am the only daughter of this lady and her son is your maternal uncle.
 Pointing to a photograph a lady tells Chetan, “I am the only daughter of this lady and her son:

 Your maternal uncle: Chatan's maternal uncle means, his mother's brother.

Merge the above two diagrams.  

 So the speaker is the mother of Chetan. Speaker is wife of Chetan's father.(chetan's father is not shown in the diagram)

Solved Example 4:
A is the brother of K, K is the brother of Q and R is the sister of Q. How is R related to A?

Simple one. From the diagram it is clear that R is sister of A.

Solved Example 5:
Introducing Harsh, Ritu said, “He is the only son of my mother’s mother.” How is Ritu related to  

Now Ritu's mother's mother means her grand mother.  Grand mother's only son is Ritu's uncle.  But we don't know Ritu is male or female so Ritu relationship with harsh cannot be determined.

Solved Example 6:
A family consists of five members: P, Q, R, S and T.   T has two sons, an unmarried daughter and a daughter-in-law. P is the brother-in-law of above-mentioned daughter-in-law. Q’s sister is not happy with Q’s wife. But P and his father support Q’s wife S.  Who is T's daughter?

From the above diagram, R is T's daughter

Solved Example 7:
Group Questions:

Directions for Questions 1 to 4 :  Read the given data carefully and solve the questions follow.

1.  A is the father of two children. B and D, Who are of different sexes.
2.  C is B’s spouse.
3.  E is the same sex as D.
4.  B and C have two children : F, who is the same sex as B, and G, who is the same sex as C.
5.  E’s mother, H, who is married to L, is the sister of D’s mother, M.
6.  E and E’s spouse. I, have two children, J and K, who are the same sex as I.
7.  No persons have married more than once and no children have been born out of wedlock. The only restrictions on marriage are that marriage to a sibling, to a direct descendant, or to more than one person at the same time is forbidden.
Solution:

We have to draw the above diagram, based on the information given in the question.  If the gender of the person is known, it is denoted by the suffix m or f.  If not know, It is denoted by x or y. We know, for example, that G is the same sex as C, so we label both x; B and therefore F are the opposite sex from C, so we label both y, and so on. Horizontal lines indicate marriage, vertical or diagonal lines indicate children.

1. F  is
a. G’s brother    b. G’s sister
c. B’s daughter    d.  D’s niece or nephew
e.  the same sex as H
Ans:  This question orients you, in case you made an unwarranted assumption about the sexes. Since we do not know B’s sex for sure, we don’t know F’s; this rules out all the wrong choices - including E, since we do know H’s sex. As the child of D’s sibling B, F is D’s niece or nephew. So option D is correct

2.  According to the rules, D can marry
a. F only    b. G only    c. J only    d.  J or K only    e.  F, J or K
Ans:  D is an x, and can therefore marry any unmarried y. So he can marry F, J, or K. Option E is correct.

3. If L and H divorced, H could marry
I.   D only      II.  F     III. D or G
a.  I only    b. II only        c.  III only    d. I or II, but not both.    e.  II or III, but not both
Ans: H is female. If x = male, H can marry D or G, so I is out. If y = male, H can marry F. Clerly H cannot marry both. (J and D are ruled out, since they are H’s direct descendants.)

4. If the generation of F and K’s parents and their siblings contains more females than males, which of the following must be true ?
a. There are more females than males in F and K’s generation.
b. J is male.
c.  A is the same sex as D.
d.  K and G are the same sex.
e.  D in H’s nephew.
Ans: This generation (the middle generation) contains three x’s and two y’s. If the more x’s are female, J, who is a y, must be male. If x = female, choices A, C, and E are untrue. Choice D can never be true.  So option B is correct.

Solved Example 8:
Directions for Questions 5 to 7 :   
In a certain society, there are two marriage groups, Red and Brown. No marriage is permitted within a group. On marriage, males become part of their wife’s group; women remain in their own group. Children belong to the same group as their parents. Widowers and divorced makes revert to the group of their birth. Marriage to more than one person at the same time and marriage to a direct descendant are forbidden.

5.  A Brown female could have had
    i.  a grandfather born Brown
    ii. a grandfather born Red.
    iii. two grandfathers born Brown
    a. I only    b. III only
    c. I and II only    d. II and III only
    e. I, II, and III

Solution:

Both parents of a Brown female are Brown, but her father was born Red. Her mother’s mother was Brown, and therefore that grandfather was born Red (I); her father’s mother was Red, and therefore that grandfather was born Brown (II). Use the following logic: if the parents were born in different groups, and the grandmothers were in the same groups, as the parents, the grandfathers must have been in different groups.  Option C

6.  A male born into the Brown group may have
    a. an uncle in either group  
    b. a Brown daughter
    c. a Brown son      
    d. a son-in-law born into the Red group
    e. a daughter-in-law in the Red group

From the above diagram it is clear that a Male born into a brown group may have Uncle in either group.  Option A correct.

7.    Which of the following is not permitted under the rules as stated ?
    a. A Brown male marrying his father’s sister  
    b. A Red female marrying her mother’s brother
    c. A man born Red, who is now a widower, marrying his brother’s widow
    d. A widower marrying his wife’s sister
    e. A Widow marrying her divorced daughter’s ex-husband.

Ans:   (A) A Brown male's mother is brown, father is born Red. So his sister is red.  So marriage permitted
(B) A Red female’s mother is Red, and the brother, whether unmarried, divorced, or a widower, is also Red. No Red may marry a Red. So not permitted.
(C) The brother of the man born Red (who as a widow, is Red again) was also born Red, so his wife (now his widow) is Brown.
(D) Any widower has reverted to his original group, while his wife’s sister is in the same group as his wife was. So marriage permitted.
(E) Any widow’s daughter is in her own group, and the ex-husband, having revered to the group of his birth, will be eligible.

Interview Reasoning questions and answer

Interview Reasoning questions and answer of Directions with explanation 

Directions

To solve directions related questions effectively, we first understand the follow diagram

TIP: When ever you are solving a direction problem, you must assume that you are at the intersection point.

A man starts walking from his house towards north and covers 15.5 km and then turns left and walks 7 km. He then turns left again and after walking 31 km again turns left and stops after 7 km. How far is he from his house?

From the above diagram we know that CD is equal to BE. and AE = BE - AB = 31 - 15.5 = 15.5

Vasu facing west moved 50 m, then he took a left-turn and moved another 100 m. He then took a left-turn and moved another 70 m. After that he took another right-turn and moved 120 m. How far is he from the starting point?

From the above diagram We need to calculat OS which is the short distance.  Now OY = 100 + 120 = 220. and XR = QR - OP = 70- 50 = 20m

Now OS=OY2+YS2−−−−−−−−−−√$OS=\sqrt{O{Y}^2+Y{S}^2}$
=(220)2+(20)2−−−−−−−−−−−√$=\sqrt{{\left(220\right)}^2+{\left(20\right)}^2}$
=48400+400−−−−−−−−−−√$=\sqrt{48400+400}$
=48800−−−−−√$=\sqrt{48800}$
= 220.9 meters

If a bear walks ten miles south, turns left and walks ten miles to the east and then turns left again and walks ten mile north and arrives at its original position, what is the color of the bear.
Tricky one.  A bear which took 2 turns after starting and came to the same position may happen only at Earth poles. Now the bear moves towards south means it started at north pole.  In the north pole bears are in white color.

Directions for 1 to 5: 

1. Agra is north of Erode and west of Calcutta.
2. Bombay is north of Agra and west of Federicktown.
3. Delhi is south and east of Agra
4. Erode is north of Faridabad and east of Delhi.5. Faridabad is north of Delhi and west of Agra.
6. Calcutta is south of Faridabad and west of Delhi.

1. Which of the towns mentioned is furthest to the northwest ?

a. Agra 
b. Bombay
c. Calcutta 
d. Erode
e. Faridabad

2. Which of the following must be both north and east of Faridabad ?
 I. Agra
 II. Calcutta
 III. Erode
a. I only 
b. II only
c. III only 
d. I and II
e. I and III

3. Which of the following towns must be situated both south and west of at least one other town ?
 a. Agra only
 b. Agra and Faridabad
 c. Delhi and Faridabad
 d. Delhi, Calcutta, and Faridabad
 e. Calcutta, Delhi, and Erode

4. Which of the following statements, if true, would make the information in the numbered statements more specific ?
 a. Calcutta is north of Delhi.
 b. Erode is north of Delhi
 c. Agra is east of Bombay.
 d. Calcutta is east of Faridabad.
 e. Bombay is north of Faridabad.

5.  Which of the numbered statements gives information that can be deduced from one or more of the other statements ?
a. 1 
b. 2
c. 3
d. 4 e. 6

 Your first instinct may be to draw a map and try to place the towns on it directly. You’ll go hopelessly wrong if you try. (This is also true for other puzzles that contain two sets of ranked variables - John runs faster and jumps higher than Tom, and so on.) First place the towns on a north-south scale and on a separate east-west scale (Diagram 1). Then, if you wish, combine these into a two-dimensional map. This isn’t necessary, but it may make the questions a little-easier. We’ve included it (Diagram 2).

1.. B Bombay is both farthest north and farthest west.

2. E Agra and Erode are north of Faridabad, while Calcutta is to the south. All three towns are east of Faridabad.

3. D This one may be easier to read from the two-dimensional map, but you can also read it from the two separate scales. Calcutta. Delhi, and Faridabad are all south and west of Erode. Faridabad is also south and west of Agra. Bombay is not such of any town. Agra is south of Bombay, but east of it.

4. A The only ambigous information in the statements concerns the north-south position of Delhi. Statements (5) and (6) tell us that Delhi and Calcutta are both south of Faridabad, but not their position in relation to each other. A would clear this up. Choices B-E can all be deduced from the statements as given.

5. C Delhi’s north-south position with respect to Agra can be deduced from statement (1), (4), and (5), without statement (3). Delhi’s east-west position with respect to Agra can be deduced from statements (1) and (6). each of the other choices is necessary to place the town it mentions either on the north-south scale on the east-west scale, or on both.